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Post Correspondence Problem with Partially Commutative Alphabets

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Language and Automata Theory and Applications (LATA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6031))

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Abstract

We introduce a version of Post Correspondence Problem (PCP, in short) generalized to words over partially commutative alphabets. Several observations are presented about the algorithmic status of the introduced problem. In particular solvability is shown for the partially commutative PCP for two special cases: the binary case of PCP (denoted by PCP(2) ), and the case with one periodic morphism. This extends solvability results for the classical PCP for these cases. Also a weaker version of PCP, named here Weak-PCP, is discussed. This version distinguishes (in the sense of solvability) the case of noncommutative from the case of partially commutative alphabets. We consider also a solvable (though NP-hard) simple version of Weak-PCP. Our solvability results demonstrate the power of Ibarra’s algorithms for reversal bounded multi-counter machines.

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References

  1. Clerbout, M., Latteux, M.: Semi-commutations. Information & Computation 73(1), 59–74 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  2. Diekert, V., Rozenberg, G.: The Book of Traces. World Scientific Publishing Co., Inc., Singapore (1995)

    Google Scholar 

  3. Ehrenfeucht, A., Karhumäki, J., Rozenberg, G.: The (generalized) Post correspondence problem with lists consisting of two words is decidable. Theor. Comput. Sci. 21, 119–144 (1982)

    Article  MATH  Google Scholar 

  4. Ehrenfeucht, A., Karhumäki, J., Rozenberg, G.: On binary equality sets and a solution to the set conjecture in the binary case. Journal of Algebra 85, 76–85 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  5. Esparza, J.: Petri nets, commutative context-free grammars, and basic parallel processes. Fundamenta Informaticae 31, 13–26 (1997)

    MATH  MathSciNet  Google Scholar 

  6. Gibbons, A., Rytter, W.: On the decidability of some problems about rational subsets of free partially commutative monoids. Theor. Comput. Sci. 48(2-3), 329–337 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  7. Halava, V., Harju, T., Hirvensalo, M.: Binary (generalized) Post correspondence problem. Theor. Comput. Sci. 276(1-2), 183–204 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  8. Harju, T., Karhumäki, J.: Morphisms. In: Handbook of formal languages, vol. 1 (1997)

    Google Scholar 

  9. Harju, T., Karhumäki, J., Krob, D.: Remarks on generelized Post correspondence problem. In: Puech, C., Reischuk, R. (eds.) STACS 1996. LNCS, vol. 1046, pp. 39–48. Springer, Heidelberg (1996)

    Google Scholar 

  10. Holub, S.: Binary equality sets are generated by two words. Int. J. Algebra (259), 1–42 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Hopcroft, J., Motwani, R., Ullman, J.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (2001)

    MATH  Google Scholar 

  12. Ibarra, O.H., Kim, C.E.: A useful device for showing the solvability of some decision problems. In: STOC ’76: Proceedings of the eighth annual ACM symposium on Theory of computing, pp. 135–140 (1976)

    Google Scholar 

  13. Ibarra, O.: Reversal-bounded multicounter machines and their decision problems. J. ACM 25(1), 116–133 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kopczyǹski, E.: Personal Communication (2009)

    Google Scholar 

  15. Kopczyński, E.: Complexity of problems of commutative grammars, draft (2009)

    Google Scholar 

  16. Lasota, S.: Personal Communication (2009)

    Google Scholar 

  17. Leroux, J.: A polynomial time Presburger criterion and synthesis for number decision diagrams. In: LICS, pp. 147–156 (2005)

    Google Scholar 

  18. Leroux, J.: Personal Communication (2009)

    Google Scholar 

  19. Matiyasevich, Y., Sénizergues, G.: Decision problems for semi-Thue systems with a few rules, pp. 523–531 (1996)

    Google Scholar 

  20. Mazurkiewicz, A.: Concurrent program schemes and their interpretations. Technical report, Aarhus University (1977)

    Google Scholar 

  21. Ochmański, E.: Recognizable Trace Languages, pp. 167–204. World Scientific Publishing Co., Inc., Singapore (1995)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097, Warszawa, Poland

    Wojciech Rytter

  2. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland

    Barbara Klunder & Wojciech Rytter

Authors
  1. Barbara Klunder
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  2. Wojciech Rytter
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Fachbereich IV - Informatik, Universität Trier, Campus II, Behringstraße, 54286, Trier, Germany

    Henning Fernau

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Klunder, B., Rytter, W. (2010). Post Correspondence Problem with Partially Commutative Alphabets. In: Dediu, AH., Fernau, H., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2010. Lecture Notes in Computer Science, vol 6031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13089-2_30

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  • DOI: https://doi.org/10.1007/978-3-642-13089-2_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13088-5

  • Online ISBN: 978-3-642-13089-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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